Equity performance, bond liquidity and corporate bond yield spreads in China

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Equity performance, bond liquidity and corporate

bond yield spreads in China

Chen, Hongming s2125064

Master Thesis for Msc Finance (2012/2013) Final version, June 2013

Number of words: 10,013

Abstract

This paper employs panel regression analysis to explore the relationship between equity performance, bond liquidity and corporate bond yield spreads in China. The results indicate that equity return has negative impacts on yield spread and the change in yield spread, while equity market volatility has positive effects. And interestingly, an improvement in liquidity widens yield spread over time within the firm level. JEL Classification: G12

Key words: yield spread, equity performance, liquidity

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Despite the rapid development of corporate bond markets in China during recent years, corporate bonds are still among the least familiar instruments for private investors.1 Besides, the market mechanism is still relatively immature compared to their western counterparts. Therefore, it is worthwhile to investigate the valuation of corporate bonds in Chinese markets.2

Investors care about the return and risk in the corporate bond investing arena during an economic downturn period. Considering the poor performance of the equity markets in China from year 2007, investors might question whether bond yields have associations with the return and volatility of equity? If the performance of equity market influences the corporate bond market, then investors might possibly anticipate the return of the corporate bond.

The performance of equity and bond is different for several reasons. When investors have positive expectations on a corporate’s future profit, stock price will rise. The bond price also increases (yield falls) as the corporate has a higher firm value thus a lower possibility to default. Kwan (1996) finds that the correlation between stock return and bond yield spread is negative. As bondholders only receive a fixed amount of payment, principal or interest, they have no rights to enjoy the extra profit. As a result, bonds benefit less than equities.

The other reason is that volatility has opposite effects on equities and bonds. According to Merton (1974), his structural model of securities pricing suggests that asset return volatility benefits stock price, as a result of the optionality offered. More volatility increases the option value. To the contrary, increasing volatility would raise the bond yield since higher volatility could lead to a higher probability of default. Campbell and Taksler (2003) find that equity volatility affects the level of corporate bond yields. Hong et al. (2012) show both investment-grade and speculative bond

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The growth rate of the capital from corporate bond markets stands at 35.68% in the first half of year 2012. The main investors are institutions. Source: Shanghai Brilliance Credit Rating & Investors Service Co., Ltd. 2 Wang et al. (2012) argue the relatively short history and specialty of Chinese corporate bond markets limit the research. There are some shortcomings of the mechanism and regulations of the bond markets, further

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returns can be predicted by the stock market performance. Since Chinese stock markets are highly speculative, it would be interesting to investigate whether the theoretical results and existing findings work on the case of the Chinese markets.

Apart from focusing on return alone, investors may also take liquidity risk into account when making investment decisions. Compared to equities, fixed-income securities are less liquid in general. Among which, corporate bonds are the least liquid. Therefore, investors require a higher yield on corporate bonds, a liquidity premium. Chen, et al. (2007) find less liquid bonds have higher yield spreads. During a crisis period, investors prefer more liquid bonds, which demonstrate a flight to liquidity.

The purpose of this thesis is to explore the relationship between equity performance, liquidity and corporate bond yield spreads. Then the main research question is raised: do equity performance and liquidity have effects on bond yield spread in China?

Since the Chinese corporate bond markets have a relatively short history, previous papers written on this topic are based on very limited samples. This thesis is used as a robustness check of the conclusions from previous papers. In addition, the thesis provides a quantitative insight for private investors who have plans to invest in the Chinese corporate bonds.

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II. Determinants of corporate bond yield spreads

Corporate bond yield spread is the additional yield over the risk-free rate of nearest maturity offered in the market.3 The yield of government bonds or the swap is considered as the risk-free rate. The spread arises because investors are subject to credit risk when they own corporate bonds. Hence a premium is required to compensate for their potential losses.

Several standard frameworks of bond pricing and yield analysis have been delivered. These models mainly concentrate on the influence of firm specific factors. Merton (1974) assumes the dynamic firm value in the perfect market can be determined by investors’ expected rate of return, volatility of firm value and corporate’s payout ratio.

The principle behind Merton’s contingent claims approach is that the corporate bondholders have the payoff of a long position in risk-free debt and a short position in a put option on the company’s asset. As soon as the company’s asset value falls below the value of debt, the option is exercised, thus the corporate bond defaults. Assuming the risk-free rate and default point (total debt amount) remaining unchanged, then the price of the corporate bond can be obtained by the Black and Scholes (1973) formula. This formula is utilized to price European options. Factors such as risk-free rate, maturity, leverage ratio and volatility of firm value theoretically contribute to the level of yield spread.

Longstaff and Schwartz (1995) find that yield spread and interest rate is negatively correlated. Leland and Toft (1996) conclude yield spread increases with maturity and leverage ratio. Flannery et al. (2012) confirm that investors’ expectations about future leverage changes have a significant impact on yield spread. Campbell and Taksler (2003) suggest that idiosyncratic equity volatility can account for as much cross-sectional differences in yield spread as credit rating. Besides, the empirical results from Campbell and Taksler (2003) show that an increase in either equity return or equity market return would lead to a lower yield spread.

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However, Collin-Dufresne et al. (2001) apply the structural form models to study the American corporate bond yield spread levels and changes, they find that the credit risk elements can neither fully explain the levels nor changes in the yield. A later study in Huang and Huang (2012) demonstrated that credit risk only contributes a small portion of yield spread.

Yield spread is also determined by factors such as macroeconomic variables. Collin-Dufresne et al. (2001) propose the slope of the term structure as an explanatory variable for yield spread.4 They state that there is a negative relationship between yield spread and the slope. The argument is that the slope provides an expectation of future rates as well as an indicator of uncertainty on the macroeconomic situation. Interestingly, Ericsson and Renault (2006) obtain a significant negative correlation between the stock index returns and yield spreads. Darwin, et al. (2012) notice that bond’s maturity, company’s leverage ratio and also the macroeconomic situation have significant effects on the levels and changes of yield spreads.

Elton et al. (2001) formally decompose yield spread into three components, expected default loss, tax premium and risk premium. They surprisingly find that expected default risk explains only a small portion of the corporate bond spread. This is because the coupons of corporate bonds would be taxed, while the coupons of government bonds are tax-free in some countries. Investors thus require additional return on corporate bonds to offset the taxation differences.

Corporate bond prices are observed to deviate from their theoretical values because of the existence of illiquidity in the market. Chen, et al. (2007) confirm that liquidity is a key non-default component of the spread. They find illiquid bonds have higher yield spreads, and an improvement in liquidity causes a significant reduction in spreads. The primary reason is illiquid instruments are relatively difficult to trade and to hedge the risk involved. In this case, illiquidity leads to a premium.

Unfortunately, the liquidity of a corporate bond is difficult to measure, which hinders the study on corporate bond yield spread. However, researchers have

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developed various methods to measure liquidity. Roll (1984) utilizes a simple implicit measure to estimate the effective bid-ask spread. Amihud and Mendelson (1986) adopt quoted bid-ask spread as the direct indicator of illiquidity. Lesmond et al. (1999) focus on trading intensity, so that they simply apply the percentage of the number of zero trading days as an illiquidity indicator.5 Amihud (2002) uses the ratio of bond return over daily trading volume. Mahanti, et al. (2008) introduce a liquidity measurement called latent liquidity, which is the weighted average turnover of the funds holding the bond. This approach characterizes investors’ liquidity preferences. Recently, Dick-Nielsen et al. (2012) develop the price dispersion to be an appropriate indicator of liquidity. All the studies demonstrate illiquidity widens yield spread.

Although all the models mentioned above state that default risks contribute to the determination of yield spread, it is difficult to measure credit risk directly. The development of new financial derivatives provides solutions to the problem. For instance, credit default swap (CDS) spread may explain the default-related component of credit spread.6 Longstaff et al. (2005) firstly develop a model that links CDS spread to corporate bonds spread. In their empirical analysis, they find although default risk is an important determinant of yield spread, other non-default factors such as liquidity and taxes also have significant influences on the determination of the spread. Dastidar and Phelps (2011) use the bond’s option adjusted spread (OAS) as a variable to build the model, and the results also confirm previous conclusions.7

To sum up, previous studies demonstrate that corporate bond yield spreads can be affected by bond specific factors, credit risk, market risk and liquidity risk. The determinants of yield spreads, as well as their effects, arguments and supporting literature are summarized in Table 1.

5 Zero trading day is defined as the day with no trading volume.

6 CDS is a swap agreement that the seller of the CDS will compensate the buyer in the event of a loan default or other credit event. The buyer of the CDS makes a series of payments (spread) to the seller and, in exchange, receives a payoff if the loan defaults. Source: Wikipedia.

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7 Table 1

Summary of yield spread determinants, their effects, arguments and literature

Factor Effect Argument Literature

Equity performance

Equity return - Higher returns indicate positive expectations and lower default risk

Campbell and Taksler (2003) Equity market return -

Equity volatility + Higher volatility leads to higher default risk

Merton (1974) Market volatility +

Liquidity - An increase in liquidity lowers

liquidity risk and thus the premium

Longstaff, et al. (2005)

Other factors

Coupon rate + Due of tax effects, higher-coupon bonds are less attractive

Elton et al. (2001)

Maturity + Risk-neutral probability of default increases with maturity

Leland and Toft (1996) Credit rating - Lower credit rating, higher yield

spreads

Universal conclusion

Leverage ratio + An increase in leverage results in higher default risk

Merton (1974) Flannery et al. (2012) Risk-free rate - A higher risk-free rate leads to a

higher risk-neutral drift, and reduces the default risk

Longstaff and Schwartz (1995) Chen, et al. (2007) Slope - The higher the slope, the higher the

expected future spot rate

Collin-Dufresne et al. (2001)

This paper aims to investigate the influence of equity performance and liquidity on corporate bond yield spreads. Based on the discussion on the determinants of yield spread, the research questions are formulated as below: (1) Does a firm’s equity return have a negative effect on bond yield spread? (2) Do firms’ equity volatility and equity market volatility have positive effects on bond yield spread? (3) Does liquidity risk have positive impacts on corporate bond yield spreads?

III. Methodology

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be used to estimate the relationship between variables. Since the data is comprised of both cross-sectional and time-series data, panel analysis is needed.

A. Regression model

1) Equity performance, liquidity and yield spreads

According to the preceding discussion on yield spread determinants, the testing model is constructed as follows:

Yield Spreadit = α0 + β1Equity performanceit + β2Liquidity Riskit +β3Bond

Charateristicsit + β4Credit Riskit + εit, (1)

where the subscript it refers to bond i and month t, εit is the residual part.

To make the model testable, these determinants are further decomposed into several independent variables. The existing literature on corporate bonds pricing discussed in Section II applies either the structural or the reduced form model to investigate yield spread. The structural form approach mainly focuses on the default risk associated with the spreads. In fact, none of the corporate bonds in China has defaulted, so the default rate and the recovery rate have no ways to calculate. Therefore, the structural model is difficult to apply. Alternatively, this research would employ the reduced form model in order to study the determinants of yield spreads. The model is presented as follows,

Yield Spreadit = α0 + β1Equity Returnit + β2Equity Volatilityit + β3Equity Market

Volatilityt + β4Turnover Ratioit + β5Trading Day Dummyit

+β6Coupon Ratei + β7Maturityit + β8Credit Rating Dummyit +

β9Leverageit + β10Slopet + εit., (2)

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The residual may be explained by other factors such as the tax rate and interest rate that are not included in this model. In the assumptions of OLS regression, the error term εit should follow a normal distribution with an expected value of zero and a

constant and finite variance. Hence there is no systematic error. In addition, the residuals are uncorrelated with each other as well independent variables.

In the aim to answer the research questions, the hypotheses are formulated as below: Hypothesis 1: H0: β1 = 0; H1: β1 < 0; Hypothesis 2: H0: β2 = 0; H1: β2 > 0; Hypothesis 3: H0: β3 = 0; H1: β3 > 0; Hypothesis 4: H0: β4 = 0; H1: β4 < 0; Hypothesis 5: H0: β5 = 0; H1: β5 < 0;

and a simultaneous test: β1 = β2 = β3 = β4 = β5 = 0.

The coefficient represents the average impact of each variable from the regression estimation. Assuming the value, which is the coefficient divided by its standard error, following a Student’s t-distribution, given a significance level, (1) if the t-statistic falls in the rejection region, the null hypothesis is rejected, and the alternative hypothesis is favored; (2) if the t-statistic is outside the rejection region, the null hypothesis cannot be rejected and the alternative hypothesis cannot be favored.

Yield spreads. Theoretically, the absolute yield spread is the additional yield of

corporate bond over the government bond rate with the same coupon rate and maturity. However, it is difficult to find the government bonds with exactly same issuance condition with each corporate bond. Instead, this research adopts the term structure of exchanges government bonds as the benchmark rate. The yield spread is calculated as the difference between the yield of corporate bond and the yield of government bond curve at the closest maturity.

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yields of two consecutive maturities are of a big difference. Yield spread will witness a significant change. And the calculated yield spread cannot reflect the actual yield spread. An effective method to eliminate the potential pitfall is to smooth the term structure. Zhu and Chen (2003), Yu and Wang (2010) indicate that the procedure of Nelson and Siegel (1987) can appropriately fit the Chinese government bond yield curve. Therefore, in the robustness check section, the Nelson-Siegel model is adopted to estimate the yield curve. A panel regression based on the Nelson-Siegel fitted yield spreads is executed. For each month, the term structure is fitted with the equation

r(t) = β0 + β1e-t/τ + β2(

𝑡 𝜏e

-t/τ

), (3)

where r(t) denotes the rate at maturity t, β0, β1 and β2 are coefficients in determining

the rate, and τ is the time constant. By plugging in the observed government bond yields in the left side of the equation, the parameters such as β0, β1, β2 and τ are

estimated by regression. Then the imaginary yield of any maturity can be obtained by inserting the decided maturity t, and the entire yield curve is plotted.

Equity return and volatility. Equity return is the monthly arithmetic return. To

estimate equity volatility, first the standard deviation of daily equity returns is calculated. The monthly equity volatility is obtained by multiplying the daily standard deviation by the square root of the number of trading days in each month. The underlying assumption is the equity return has a normal distribution.

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benchmark market return. In addition, excess return is dependent on market return, including both as independent variables in the regression model is inappropriate. The practical argument is that investors care more about absolute return rather than relative return. The other difference is the estimation window for equity return and standard deviation. Zhang and Li (2003) state that Chinese equity markets are weak-form efficient, so the past securities’ performance and information have no predictive power about the future performance. For this reason, the return and the standard deviation of the trading month are used as equity performance metrics.

Turnover Ratio and Trading Day Dummy. Goyenko et al. (2009) summarize

various metrics to measure liquidity. Liquidity can be measured via three aspects: trading intensity, trading size and trading cost. Most studies on bond liquidity quote the bid-ask spread as an efficient liquidity proxy. However, Mahanti et al. (2008) argue that this proxy is only feasible in markets that are reasonably liquid, having continuously trading activities. Considering the low liquidity and degree of transparency of Chinese corporate bond markets, some proxies such as bid-ask spreads are difficult to obtain and the proxies are not effective.8 Hence, two simple ratios are adopted as liquidity proxies. That is a

Turnover ratio = total trading volume of the month

total volume outstanding , and a (4)

Trading day ratio = number of positive-volume days - number of zero-volume days number of total trading days . (5)

These two ratios are the modified versions of low-frequency liquidity measures mentioned in Goyenko et al. (2009). Turnover ratio is used to indicate the transaction size component of liquidity. Trading day ratio provides the indirect measure of transaction intensity.

Leverage ratio. Leverage ratio is an important accounting data which reflects a

firm’s capital structure and its potential risk. It is defined as

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Leverage ratio = _{total value of asset}total value of debt . (6)

A high leverage ratio means a firm is highly levered, and the firm has a high possibility to go into stressed situation, hence a high spread. As the leverage ratio is only published in corporates’ quarterly report, a linear interpolation scheme is employed to estimate monthly leverage ratio by using quarterly leverage ratio.

2) Equity performance, liquidity and yield spread changes

In addition, another regression is conducted to investigate whether the changes in equity performance and liquidity have impacts on the changes of corporate bond yield spreads. The regression model is as follows:

ΔYield Spreadit = α0 +β1Equity Returnit + β2ΔEquity Volatilityit + β3ΔEquity

Market Volatilityt + β4ΔTurnover Ratioit + β5ΔTrading Day

Ratioit + β6ΔCredit Ratingit + β7ΔLeverageit + β8ΔSlopet + εit.

(7) where Δ is defined as the difference between two consecutive observations of each variable. Except equity return, all the other variables are measured as the difference between the values of two consecutive periods, which indicate the level of change in the variables. εit again represents the unexplained part of variations in yield spread

changes.

Collin-Dufresne et al. (2001) confirm the equity return and change in slope have negative effects on the change in yield spreads. While the change in equity volatility and change in leverage ratios have positive impacts. In order to test the potential effects, the following hypotheses are constructed:

Hypothesis 1: H0: β1 = 0; H1: β1 < 0;

Hypothesis 2: H0: β2 = 0; H1: β2 > 0;

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Hypothesis 5: H0: β5 = 0; H1: β5 < 0;

and a simultaneous test: β1 = β2 = β3 = β4 = β5 = 0.

This procedure aims to argue that equity performance and liquidity has influence not only on the level of yield spreads, but also on the changes in yield spread. Moreover, these hypotheses are used to check whether the relationship between yield spread, equity performance and liquidity is consistent with that from Equation (2).

B. Panel analysis9

Panel data consists of both cross-sectional and time-series dimensional data. The simplest way to analyze panel data is to run a pooled regression with the following equation:

yit = α + βxit + μit, (8)

where it refers to cross-sectional element i and time-series element t. y and x are dependent variable and independent variable respectively. α is the intercepts, β is the estimated coefficient (slope), and μ is the disturbance term.

The pooling procedure assumes that the average values of variables and the relationships between them are constant both over time and across sections. With respect to this research, a pooled regression assumes the intercepts are the same for each firm and at the point in time. Nevertheless, this universal equation cannot examine how the relationship between the variables changes over time. In order to test whether within a single bond, equity performance and liquidity have impacts on the level of yield spreads, cross-sectional variations should be removed. Brooks (2008) provides two feasible methods, which are the fixed effects model and the random effects model.

The fixed effects model decomposes the residual into an individual effect

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intercept μi and a disturbance part νit that varies over both time and cross-section, then

Equation (8) becomes

yit = α + βxit + μi + νit. (9)

The essence of fixed effects model is that it allows the intercept in the regression to vary across sections but not over time. The estimated slope is still constant in both time-series and cross-sectional dimensions.

The random effects model also allows intercept to differ cross-sectionally but to keep constant over time. However, in the random effects model, the intercept term is assumed to be generated from a global intercept term α plus a random variable εi which varies cross-sectionally but is constant over time, Equation (8) is rewritten as:

yit = α + βxit + εi + νit. (10)

Brooks (2008) states that the random effects model is more appropriate when the data in the sample is assumed to be randomly selected from a population, while the fixed effect model is preferred when the data effectively constitutes the entire population. A major drawback of the random effects model is that the estimated parameter is unbiased and consistent only if the residual is uncorrelated with the independent variables. An approach to detect the potential relationship between the residual and independent variable is applying the Hausman test. If the null hypothesis which states no correlation between residual and explanatory variables is rejected, the fixed effects model is more appropriate. Otherwise, the random effects model should be chosen.

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regression with equity variables but without liquidity variables; (3) regression without equity variables but with liquidity variables; (4) regression with both equity and liquidity variables. Secondly, a Hausman test is run to determine whether to apply the fixed effects model or the random effect model. Then the chosen model is employed to eliminate the cross-sectional variations.

IV. Data

The data is collected from the China Central Depository and Clearing database (CCDC) and the FinChina (FC) database.10 CCDC is a non-bank financial institution jointly founded by People’s Bank of China and the Ministry of Finance aimed to establish an efficient bond market. CCDC is the authority in the bond market, and FinChina is a listed company which provides all kinds of financial data. The CCDC database contains bond and issuer’s unique characteristics such as the coupon rate, maturity, credit rating. The database also includes transaction data. However, the data from the CCDC database is only available after August 2011. When data is not available from the CCDC database, the needed data is drawn from the FC database. The equity and market data are obtained from FC database as well.

There are three sectors of bond markets, namely interbank or wholesale market, over-the-counter (OTC) market and the exchanges. For the first two markets, corporate bonds are only traded between financial institutions. While the exchanges market provides the private investors with access to corporate bonds investment.

In China, corporate bonds are further divided into two categories: corporate bonds and enterprise bonds. However, these two definitions are interchangeable in the rest of the world. The most distinct difference between these two categories is that corporate bonds are all issued by state-owned corporations. To some extent, corporate bonds are similar to government bonds because of the governmental guarantees. Besides, the regulations for corporate bond are more restrictive, and the issuance size is determined by the China National Development and Reform Commission. From

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this perspective, enterprise bonds are more similar to the corporate bonds in the traditional view. Therefore, this paper focuses on the study of Chinese enterprise bond trading on at the exchanges. To avoid confusion, corporate bonds are referred to the enterprise bonds throughout the paper.

The sample consists of fixed-rate nonconvertible RMB-denominated corporate bonds listed in either Shanghai or Shenzhen exchanges. Since the first corporate bond was issued at the end of 2007, such relatively short history limits the sample size. There is only five-year data, in the period from 2008 to 2012. The number of issued bonds almost double every year, and finally there are 369 bonds outstanding at the end of 2012 excluding those that have expired.

Chinese corporate bonds market witness extreme illiquidity as mentioned by Min et al. (2011). Though monthly data is used in my thesis, turnover ratios are quite low in most cases. In consideration of such low liquidity, the samples that are suspicious to be dummy bonds are excluded. The dummy bonds here are defined as the bonds that have trading volume in their issuance period, but in later stages, have no trading activities at all. In addition, the bonds without trading for over 12 months are eliminated as well. Bonds with age less than 6-month are also dropped. They are treated as outliners when we estimate the relationship between yield spreads and liquidity.

Some data is problematic as the yield spreads are negative, such data is removed. The potential reason is that there is excess short-term demand of corporate bonds at the initiation of exchange enterprise bond market. Such excess demand induces lower yield of corporate bond than that of the government bond with similar maturities. The fact indicates that factors other than credit risk account for corporate bond yield spread in China.

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There are not authoritative credit rating agencies in China, thus the credit ratings recommended by the FC database are adopted. One outstanding feature is that all corporate bonds have high credit ratings, and all bonds are in the investment-grade category. The phenomenon is result from only corporates with high quality would be granted the rights to issue bonds. Since there are only four categories of credit ratings, each rating category is assigned as a dummy, CRD1 for AA-, CRD2 for AA, CRD3 for AA+ and CRD4 for AAA bonds.

The descriptive statistic of yield spreads classified by credit rating is presented in Table 2. The yield spreads are sorted into different credit rating categories and further classified by year and maturity. The short-term bonds are the bonds with maturity less than 3 years. Medium maturity bonds are bonds with remaining life between 3 to 5 years. Bonds with maturity over 6 years are grouped as long-term bonds. The longest maturity is 15 years.

Though the procedure to rate a bond is unknown, yield spreads are significantly affected by credit ratings. Bonds with higher credit rating generate lower spreads. Overall, the average yield spread of AAA, AA+, AA, AA- rating corporate bonds is 158, 249, 291, 412 basis points respectively. In addition the average levels of yield spreads with these four groups are plotted from 2008 till 2012, which is illustrated in Figure 1. The yield spreads of AAA bonds behave less volatile than other groups with lower ratings. The yield spreads of all categories reach high levels as the financial crisis occurred.

It is interesting to see how the equity market interacts with the corporate bond market. The CSI300 index is chosen as the benchmark market portfolio rather than Shanghai Composite index. The CSI300 index is a capitalization-weighted index aimed to track the performance of 300 largest A shares listed in Shanghai or Shenzhen exchanges. The capitalization of the CSI300 index constituent stocks is over 70% of the total capitalization of the stock market.11 Because the corporate bonds are traded

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18 Table 2

Descriptive statistics of corporate bond yield spreads in Chinese exchanges markets

The descriptive statistics of corporate bond yield spreads are reported below using monthly data from 2008 to 2012. Yield spreads are in basis points and calculated as the difference between the bond yields and the benchmark government bond yields with closest maturity. The sample consists of 17, 47, 68, 129 and 216 outstanding corporate bonds in Year 2008, 2009, 2010, 2011 and 2012 respectively. The total amount of transaction is 4,037, with 127, 280, 623, 949, 2,062 transactions in Year 2008, 2009, 2010, 2011 and 2012 respectively.

AAA AA+ AA AA-

Mean Med Max Min SD Mean Med Max Min SD Mean Med Max Min SD Mean Med Max Min SD

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19 Figure 1

Average corporate bond yield spreads

The figure displays the average corporate bond yield spreads from year 2008 to year 2012. The average yield spread is calculated as the arithmetic mean of the yields of the corporate bonds with same credit ratings recommended by FC database. The horizontal axis represents the date, and the vertical axis is the level of yield spreads, measured in basis points.

in either exchange, the CSI300 index is more appropriate.

The aggregate level of yield spreads and the CSI300 index are plotted in Figure 2. At the first glance, yield spreads and the index are negatively correlated. The reason is obvious. When the stock index decreases, the value of companies fall, this triggers a higher chance of default. Also, investors may have a pessimistic attitude towards the economy, so that they might choose more liquid assets as alternatives to reduce the potential liquidity risk. As a result, the yield spread rises. It is also worthwhile to observe that yield spreads reached a peak, and the CSI300 index got to a trough in the end of 2008 as the U.S. subprime crisis occurred. Then the yield spreads decreased, and the CSI300 index gradually recovered as a result of Chinese government’s 4-trillion economy stimulation plan. However, the yield spreads increased and index fell again from the middle of 2011 because of European sovereign debt crisis.

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20 Figure 2

Aggregate corporate bond yield spreads versus the CSI 300 index

The figure display the aggregate corporate bond yield spreads and the CSI300 index from year 2008 to year 2012. Aggregate yield spread is the arithmetic mean of all corporate bond yield spreads. Both yield spreads with and without term structure fitted via Nelson-Siegel procedure are plotted. The horizontal axis represents date, the left vertical axis is the level of yield spreads, measured in basis points, and the right vertical axis is the level of index.

with and without the Nelson-Siegel fitted procedure. This indicates that the term structure of government bond yield is smooth, and there is no big difference between the yields of two consecutive maturities.

Corporate bonds are subject to interest rate risk. Therefore, spot rate and the slope of the term structure are regarded as interest rate indicators. Spot rate represents the current risk-free rate, and the slope implies investors’ expectation on the future macroeconomic and future spot rates. However, these two variables are highly correlated. The duration of corporate bond is more sensitive to the discount rates with different maturities rather than a single spot rate. Therefore, this research only includes the slope as an explanatory variable.

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1, and these ratios are categorized into three groups, hence three trading day dummies (TDD) are introduced: TDD1 for ratios above 0.33, which represents the most liquid bonds; TDD2 for ratios between -0.33 and 0.33, which stands for bonds with medium liquidity; TDD3 for ratios below -0.33, which represents the least liquid bonds. The distributions of equity volatility and turnover ratio are positive skew, hence a log transformation is performed to these two variables.

V. Results

A. Yield spreads, equity performance and liquidity risk

The results of the pooled OLS regressions are exhibited in Table 3. The table includes the coefficients of each variable with the corresponding t-statistics. The adjusted R-squared and F-statistics associated with the regressions are reported in the table as well. The results of the all-in regression model are shown in Column 4.

The coefficient of equity return is negatively significant, so the null hypothesis is rejected. Therefore, the impact of equity returns on yield spreads are negative as expected and the result is significant. The result supports the conclusions from Kwan (1996), Campbell and Taksler (2003). This is because an increase in equity return raises the firm value, the distance-to-default is subsequently widened, which results in a decrease in the probability of default, hence the yield spread falls. Though the result is statistically significant, it is not economically significant. With each one percent increase in monthly equity return, yield spreads decrease by only 0.18 basis points.

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22 Table 3

Determinants of corporate bond yield spreads using pooled OLS regression

The regressions are based on the unbalanced panel data from 2008 to 2012. The numbers in the parentheses are corresponding t-statistics. An asterisk means significance at 5 percent level and two asterisks means significant at 1 percent level.

Regression Model

1 2 3 4

Equity performance metrics

Equity return -0.0017

(-1.88)

-0.0018 (-2.01)* Equity volatility (log) 0.0902

(1.21)

0.0634 (0.85) Equity market volatility (log) -0.0292

(-0.54)

-0.0445 (-0.83)

Liquidity metrics

Turnover ratio (log) 0.0405

(3.98)** 0.0403 (3.95)** TDD 1 (high liquidity) 0.0537 (1.84) 0.0556 (1.91) TDD 2 (medium liquidity) 0.0005 (0.02) 0.0027 (0.10) Other variables Coupon rate 0.3866 (27.75)** 0.3848 (27.37)** 0.3622 (24.41)** 0.3611 (24.19)** Maturity -0.0091 (-1.88) -0.0095 (-1.95) -0.0046 (-0.92) -0.0048 (-0.96) CRD 1 (AA-) 1.4085 (19.42)** 1.4033 (19.30)** 1.3891 (18.84)** 1.3865 (18.77)** CRD 2 (AA) 0.8084 (24.71)** 0.8015 (24.25)** 0.7918 (23.36)** 0.7860 (23.01)** CRD 3 (AA+) 0.5587 (19.43)** 0.5520 (18.93)** 0.5577 (18.85)** 0.5525 (18.46)** Leverage ratio -0.0063 (-7.86)** -0.0063 (-7.89)** -0.0057 (-7.11)** -0.0057 (-7.11)** Slope (10-year – 2-year

government bond yield)

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cannot fully represent the risks involving in the company, and the equity risk may not be transferred to the corporate bond markets. Another fact accounting for the insignificant relationship is the illiquidity of Chinese bond markets. The equity risk cannot be immediately reflected in yield spread.

It is notable that the coefficients of liquidity metrics have opposite signs. If we look at the signs of liquidity metrics, though only turnover ratio is significant, we may draw the conclusion that an improvement in liquidity results in higher yield spread. However, the impact is quite limited. One percent increase in monthly turnover ratio would increase the yield spread by only 0.04 basis points. These disappointing results can be due to the chosen liquidity proxies and facts about Chinese corporate bonds market. Firstly, though turnover ratio is a simple and popular liquidity metric in measuring the transaction size, Barinov (2012) argues that turnover ratio is more about firm-specific uncertainty rather than liquidity risk. He states that the issuer with high turnover ratio also has high uncertainty, thus the volatility rise. Volatility theoretically has positive impacts on yield spreads. In addition, turnover ratio and trading day ratio can be interfered with the potential pledge-style Repo. Such transactions increase both these two ratios, but the increase actually has no connection with bond liquidity.

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longer maturity, so the maturity and yield spread is negatively correlated.

There are theoretical and practical reasons account for the opposite sign of leverage ratio coefficient. In capital structure theory, the company which utilizes more debt as financing would benefit from tax-shield, and increase the company’s value until the optimal capital structure is reached.12 As a matter of fact, no corporate bonds have defaulted yet in China, and most firms have strong financing and debt repayment capability, the possibility of default is relatively low. As a result, investors would consider higher leverage within a reasonable range as a positive signal.

Overall, the results of the regression model are jointly significant with a high

F-statistic. However, when we compare the adjusted R-squared in these four

columns, we have the notion that both equity variables and liquidity variables have little explanatory power of variations in yield spreads. In Column 1, we can see the control variables alone can account for over 50 percent variations in the yield spreads. In other words, these variables have significant impacts on determining the level of yield spreads. Adding either equity variables or liquidity variables in the regression model (Column 2 and Column 3) does not significantly increase the adjusted R-squared. The combination of these variables only account for 0.3 percent increase in adjusted R-squared.

There are several reasons for the low explanatory power of equity performance variable and liquidity variable. As the Chinese equity market is highly speculative and subject to short-term shocks, the equity performance cannot well reflect the intrinsic value and risk of listing companies. Thus equity performance cannot explain much variation in yield spread. As mentioned before, the chosen liquidity proxies in this thesis cannot efficiently demonstrate the actual level of corporate bond liquidity, for this reason, the adjusted R-squared is low.

In the previous regressions, the results show that the equity return and turnover ratio would make the yield spreads differ across issuers, while volatility and trading

12

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day ratio do not have effects. The underlying implication is that firms with higher equity return have lower yield spreads. Is this finding consistent within a single company over time? In other words, does the company have lower spread when its equity return is higher? To investigate, the fixed effects model or random effects model should be performed to address this problem.

The result from the Hausman test is exhibited in the appendix. The result shows that the null hypothesis is rejected, so there are correlations between the disturbance term and the independent variables. Hence the fixed effects model is more appropriate. This regression also removes the pure cross-sectional variations such as coupon rate. The results of such regressions are reported in Table 4.

Apart from the results from equity variables, other results are almost the same as those of the pooled OLS regressions. Within a single company, though the coefficients of equity return are negative, they are not significant. Hence, when the firm has higher equity return, yield spread does not decrease. The effect of equity volatility is positive but no significant. The result indicates that equity performance has no influence on yield spread over time. The equity performance cannot imply the intrinsic firm value and the firm’s capability to repay debt. Therefore, the relationship between yield spread and equity performance is ambiguous.

Equity market volatility has positive effects on the yield spreads within the firm-level. Each one percent increase in equity market volatility contributes to 0.11 basis points increase in yield spread. In the pooled OLS regression, each investor has the same market risk no matter which bonds they hold, hence the market volatility cannot account for the variations in yield spreads. While in the fixed effects model, as the cross-sectional variations are removed, market volatility can explain the variations in yield spread over time. In the period that market exhibits high volatility, the yield spread is widened. This finding corresponds with the conclusions from Campbell and Taksler (2003).

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26 Table 4

Regressions with fixed effects model

The regressions are based on the unbalanced panel data from 2008 to 2012. The regressions employ the fixed effects model to remove the cross-sectional variations. The numbers in the parentheses are corresponding t-statistics. An asterisk means significance at 5 percent level and two asterisks means significant at 1 percent level.

1 2 3 4

Equity return -0.0011 (-1.46)

-0.0013 (-1.74) Equity volatility (log) 0.2587

(2.35)*

0.1863 (1.70) Equity market volatility (log) 0.1224

(2.54)*

0.1141 (2.38)*

Turnover ratio (log) 0.0318 (3.12)** 0.0291 (2.84)** TDD 1 (high liquidity) 0.2049 (5.92)** 0.2060 (5.96)** TDD 2 (medium liquidity) 0.0613 (2.33)* 0.0628 (2.39)* Other variables Maturity -0.0086 (-0.66) -0.0348 (-2.30)* -0.0238 (-1.83) -0.0445 (-2.96)** CRD 1 (AA-) 1.3271 (7.89)** 1.3161 (7.82)** 1.3428 (8.05)** 1.3373 (8.01)** CRD 2 (AA) 0.7121 (6.30)** 0.7177 (6.36)** 0.7111 (6.35)** 0.7168 (6.40)** CRD 3 (AA+) 0.3819 (4.92)** 0.3889 (5.01)** 0.3938 (5.12)** 0.3998 (5.19)** Leverage ratio -0.0054 (-2.02)* -0.0050 (-1.90) -0.0053 (-2.00)* -0.0050 (-1.90) Slope (10-year – 2-year

government bond yield)

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coefficients are jointly significant. By applying the fixed effects model, the adjusted

R-squared increases. The fixed effects model can better explain the differences in

yield spreads than the pooled OLS model. However, when comparisons are made between these four columns, equity performance and liquidity still have little explanatory power. The combination use of equity performance and liquidity variables only contributes to 0.6 percent increase in the adjusted R-squared.

Till now, the results demonstrate that equity return accounts for a portion of variation in yield spreads across firms, and the effect is negative. Equity market volatility has positive effects on the yield spread within a single company. Interestingly, turnover ratio and trading day ratio have positive impacts on yield spread, which indicates that an improvement in liquidity increases yield spread. This finding is opposite to those in the existing literature.

B. Yield spread changes, equity performance and liquidity

The changes in equity performance and liquidity could have influences on the changes in yield spread. To see this, the results of regressions with yield spread changes are reported in Table 5. The results in Column 1 are from the pooled OLS regression, and those that in Column 2 are run with the fixed effects model.

The results of both regressions are similar. The table demonstrates that the coefficient of equity return is negatively significant, and the coefficient of change in equity market volatility is positively significant. These findings demonstrate that equity return and market volatility affect not only yield spread, but also change in yield spreads. Since equity volatility cannot reflect the actual volatility of the firm value, the change in equity volatility has no significant relationship with change in yield spreads.

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28 Table 5

Regression with yield spread changes

The regressions are based on the unbalanced panel data from 2008 to 2012. The numbers in the parentheses are corresponding t-statistics. An asterisk means significance at 5 percent level and two asterisks means significant at 1 percent level.

Pooled OLS Fixed effects

Equity return -0.0029 (-5.00)** -0.0030 (-4.96)** ΔEquity volatility -0.0012 (-0.66) -0.0011 (-0.55) ΔEquity market volatility 0.0018

(2.42)* 0.0020 (2.47)* Liquidity metrics ΔTurnover ratio 0.0001 (0.12) 0.0001 (0.15) ΔTrading day ratio 0.0445

(2.82)** 0.0436 (2.62)** Other variables ΔCredit rating -0.1314 (-1.43) -0.1596 (-1.62) ΔLeverage ratio -0.0049 (-0.77) -0.0013 (-0.17) ΔSlope (10-year – 2-year government bond

yields) 0.0305 (0.72) 0.0411 (0.91) Constant -0.0241 (-3.81)** -0.0243 (-3.73)** No. of observations 2,833 2,833 Adjusted R2 0.018 0.046 F-statistic 5.03** 0.49

statistically significant impact on change in yield spread. The change in slope of the term structure does not significantly associate with change in yield spread, as a portion of market risk is reflected in the equity market volatility.

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29 kurtosis in the distribution of the error term.

C. Robustness checks with the Nelson-Siegel model

The absolute yield spread is the difference between the corporate bond yield and the government bond yield with similar maturity. The observed government bond yield only has observations of whole-year yield. Thus if there is a big difference between the yields of two closest maturities, yield spread witnesses a significant change. And the calculated yield spread cannot reflect the actual level of yield spread that the corporate bond should have. Besides, such change is not due to changes in equity performance and liquidity, which weakens the explanatory power of the regression model in Equation (2). As robustness checks, the approach of Nelson and Siegel (1987) is employed to fit the term structure of exchanges government bonds. By applying this method, yield curve is smoothed and the potential pitfall is eliminated as well. This procedure requires fitting 60 yield curves (60 months). Then fitted yield spreads are obtained by subtracting the fitted government bond yield from the bond yield. The regression results are presented in Table 6.

The aggregate yield spread curves with and without the Nelson-Siegel procedure are plotted in Figure 2. As shown, there is not big difference between these two curves. Therefore, the results in Table 6 are similar to that from Table 3 and Table 4, only a small variation in size of the coefficients and the corresponding

t-statistics.

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30 Table 6

Regression with the Nelson-Siegel fitted yield spreads

The regressions are based on the unbalanced panel data from 2008 to 2012. The numbers in the parentheses are corresponding t-statistics. An asterisk means significance at 5 percent level and two asterisks means significant at 1 percent level.

Pooled OLS Bond fixed effects

Equity return -0.0020

(-2.29)*

-0.0015 (-1.99)* Equity volatility (log) 0.0685

(0.91)

0.2130 (1.93) Equity market volatility (log) -0.0276

(-0.51)

0.1358 (2.82)**

Turnover ratio (log) 0.0459 (4.43)** 0.0266 (2.58)** TDD 1 (high liquidity) 0.0475 (1.61) 0.2041 (5.88)** TDD 2 (medium liquidity) 0.0055 (0.21) 0.0632 (2.40)** Other variables Coupon rate 0.3542 (23.44)** N/A N/A Maturity -0.0019 (-0.38) -0.0461 (-3.05)** CRD 1 (AA-) 1.3916 (18.60)** 1.3060 (7.79)** CRD 2 (AA) 0.7835 (22.66)** 0.7072 (6.29)** CRD 3 (AA+) 0.5647 (18.64)** 0.4028 (5.21)** Leverage ratio -0.0063 (-7.69)** -0.0053 (-2.73)** Slope (10-year – 2-year government bond

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VI. Conclusion

This paper aims to explore the relationship between equity performance, liquidity and corporate bond yield spreads. Firstly, the determinants of yield spreads based on the previous literature are investigated. Secondly, a regression model and a panel analysis technique are implemented to a dataset of five-year observations. The empirical results show that equity return account for a portion of variation in yield spread across issuers, but not within a single firm over time, and its impact is negative. While equity market volatility has positive effects on the yield spread within a single company but not across companies. Interestingly, higher liquidity leads to higher yield spread in the sample, but the findings are not conclusive. As for the determinants of yield spread changes, the results indicate equity return has negative effects, and change in equity market volatility has positive impacts. No conclusion is drawn regard to the relation between the change in liquidity and change in yield spread.

One thing that should be noticed is the explanatory power of equity performance and liquidity is not strong. About 50 percent of the variations in yield spread are explained by other independent variables. Besides, though the relationships between equity performance, liquidity and yield spread are statistically significant, they are not significant economically. Investors should be aware that equity performance has impacts on yield spread, but the impacts are limited. Investors could invest in corporate bonds in a bear stock market for protection, unless there is a large jump in the equity performance.

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Appendix

Correlation matrix

YS ER LOGσ LOGσCSI300 LOGTO TDD1 TDD2 MATURITY COUPON CRD1 CRD2 CRD3 LEVERAGE SLOPE

YS 1.000 -0.017 0.183 -0.016 0.414 0.240 -0.077 -0.186 0.684 0.331 0.418 0.035 -0.137 -0.107 ER -0.017 1.000 0.053 -0.015 0.029 0.025 0.016 -0.035 0.015 0.034 -0.026 0.002 0.013 0.035 LOGσ 0.183 0.053 1.000 0.191 0.193 0.156 -0.062 0.025 0.286 0.145 0.109 0.068 0.073 0.336 LOGσCSI300 -0.016 -0.015 0.191 1.000 0.029 0.048 -0.005 0.089 0.009 0.029 -0.032 -0.022 0.028 0.020 LOGTO 0.414 0.029 0.193 0.029 1.000 0.408 0.075 -0.254 0.459 0.190 0.283 -0.001 -0.160 0.023 TDD1 0.240 0.025 0.156 0.048 0.408 1.000 -0.428 -0.103 0.383 0.153 0.135 -0.115 -0.015 0.169 TDD2 -0.077 0.016 -0.062 -0.005 0.075 -0.428 1.000 0.057 -0.125 -0.085 -0.038 0.039 -0.030 -0.029 MATURITY -0.186 -0.035 0.025 0.089 -0.254 -0.103 0.057 1.000 -0.229 -0.048 0.033 -0.175 0.094 0.141 COUPON 0.684 0.015 0.286 0.009 0.459 0.383 -0.125 -0.229 1.000 0.411 0.412 -0.015 -0.019 0.068 CRD1 0.331 0.034 0.145 0.029 0.190 0.153 -0.085 -0.048 0.411 1.000 -0.140 -0.124 0.045 0.095 CRD2 0.418 -0.026 0.109 -0.032 0.283 0.135 -0.038 0.033 0.412 -0.140 1.000 -0.494 -0.124 -0.054 CRD3 0.035 0.002 0.068 -0.022 -0.001 -0.115 0.039 -0.175 -0.015 -0.124 -0.494 1.000 0.022 -0.041 LEVERAGE -0.137 0.013 0.073 0.028 -0.160 -0.015 -0.030 0.094 -0.019 0.045 -0.124 0.022 1.000 0.115 SLOPE -0.107 0.035 0.336 0.020 0.023 0.169 -0.029 0.141 0.068 0.095 -0.054 -0.041 0.115 1.000 YS = yield spread; ER = equity return;

LOGσ = equity volatility after the log transformation;

LOGσCSI300 = equity market volatility after the log transformation; LOGTO = turnover ratio after the log transformation;

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Hausman test

Test Summary Chi-Sq. Statistic Chi-Sq. d.f. Prob. Cross-section random 79.893 12.000 0.000

Cross-section random effects test comparisons:

Variable Fixed Random Var(Diff.) Prob.

Equity performance, bond liquidity and corporate bond yield spreads in China